Olivia is told that the circumference of a circle is equal to 8pi How can she use this value to calculate the area of the circle without first, finding the radius of the circle?

Answer 1

To calculate the area of a circle using the circumference, Olivia can use the formula:

A = (C²) / (4π)

where A is the area and C is the circumference.

Given that the circumference is 8π, Olivia can substitute this value into the formula to determine the area:

A = ((8π)²) / (4π)

Simplifying the expression inside the brackets, we have:

A = (64π²) / (4π)

The π in the numerator and denominator cancels out, leaving:

A = 16π

Therefore, the area of the circle is 16π.